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Relevant bibliographies by topics / Computable mathematics

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Academic literature on the topic 'Computable mathematics'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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Journal articles on the topic "Computable mathematics"

1

KHOUSSAINOV, BAKHADYR, STEFFEN LEMPP, and THEODORE A. SLAMAN. "COMPUTABLY ENUMERABLE ALGEBRAS, THEIR EXPANSIONS, AND ISOMORPHISMS." International Journal of Algebra and Computation 15, no. 03 (2005): 437–54. http://dx.doi.org/10.1142/s0218196705002281.

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Computably enumerable algebras are the ones whose positive atomic diagrams are computably enumerable. Computable algebras are the ones whose atomic diagrams are computable. In this paper we investigate computably enumerable algebras and provide several algebraic and computable theoretic distinctions of these algebras from the class of computable algebras. We give a characterization of computably enumerable but not computable algebras in terms of congruences and effective conjunctions of [Formula: see text]-sentences. Our characterization, for example, shows that computable conjunctions of nega

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NIES, ANDRÉ, and ANDREA SORBI. "Calibrating word problems of groups via the complexity of equivalence relations." Mathematical Structures in Computer Science 28, no. 3 (2016): 457–71. http://dx.doi.org/10.1017/s0960129516000335.

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(1) There is a finitely presented group with a word problem which is a uniformly effectively inseparable equivalence relation. (2) There is a finitely generated group of computable permutations with a word problem which is a universal co-computably enumerable equivalence relation. (3) Each c.e. truth-table degree contains the word problem of a finitely generated group of computable permutations.

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Hirschfeldt, Denis R. "Degree Spectra of Relations on Computable Structures." Bulletin of Symbolic Logic 6, no. 2 (2000): 197–212. http://dx.doi.org/10.2307/421207.

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There has been increasing interest over the last few decades in the study of the effective content of Mathematics. One field whose effective content has been the subject of a large body of work, dating back at least to the early 1960s, is model theory. (A valuable reference is the handbook [7]. In particular, the introduction and the articles by Ershov and Goncharov and by Harizanov give useful overviews, while the articles by Ash and by Goncharov cover material related to the topic of this communication.)Several different notions of effectiveness of model-theoretic structures have been invest

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NIES, ANDRÉ, and PAUL SHAFER. "RANDOMNESS NOTIONS AND REVERSE MATHEMATICS." Journal of Symbolic Logic 85, no. 1 (2019): 271–99. http://dx.doi.org/10.1017/jsl.2019.50.

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AbstractWe investigate the strength of a randomness notion ${\cal R}$ as a set-existence principle in second-order arithmetic: for each Z there is an X that is ${\cal R}$-random relative to Z. We show that the equivalence between 2-randomness and being infinitely often C-incompressible is provable in $RC{A_0}$. We verify that $RC{A_0}$ proves the basic implications among randomness notions: 2-random $\Rightarrow$ weakly 2-random $\Rightarrow$ Martin-Löf random $\Rightarrow$ computably random $\Rightarrow$ Schnorr random. Also, over $RC{A_0}$ the existence of computable randoms is equivalent to

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Richman, Fred, and Oliver Aberth. "Computable Calculus." American Mathematical Monthly 109, no. 9 (2002): 862. http://dx.doi.org/10.2307/3072391.

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Morozov, A. S., and M. A. L’vova. "On computable formal concepts in computable formal contexts." Siberian Mathematical Journal 48, no. 5 (2007): 871–78. http://dx.doi.org/10.1007/s11202-007-0089-y.

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Ivanova, Z. K., and M. Kh Faizrahmanov. "Weak reducibility of computable and generalized computable numberings." Sibirskie Elektronnye Matematicheskie Izvestiya 18, no. 1 (2021): 112–20. http://dx.doi.org/10.33048/semi.2021.18.035.

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Downey, Rodney G., Matthew Harrison-Trainor, and Alexander Melnikov. "Relativizing computable categoricity." Proceedings of the American Mathematical Society 149, no. 09 (2021): 3999–4013. http://dx.doi.org/10.1090/proc/15471.

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Harrison-Trainor, Matthew, Alexander Melnikov, and Russell Miller. "On Computable Field Embeddings and Difference Closed Fields." Canadian Journal of Mathematics 69, no. 6 (2017): 1338–63. http://dx.doi.org/10.4153/cjm-2016-044-7.

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AbstractWe investigate when a computable automorphism of a computable field can be effectively extended to a computable automorphism of its (computable) algebraic closure. We then apply our results and techniques to study effective embeddings of computable difference fields into computable difference closed fields.

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Bridges, Douglas S. "Constructive mathematics: a foundation for computable analysis." Theoretical Computer Science 219, no. 1-2 (1999): 95–109. http://dx.doi.org/10.1016/s0304-3975(98)00285-0.

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Dissertations / Theses on the topic "Computable mathematics"

1

Rute, Jason. "Topics in algorithmic randomness and computable analysis." Research Showcase @ CMU, 2013. http://repository.cmu.edu/dissertations/260.

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This dissertation develops connections between algorithmic randomness and computable analysis. In the first part, it is shown that computable randomness can be defined robustly on all computable probability spaces, and that computable randomness is preserved by a.e. computable isomorphisms between spaces. Further applications are also given. In the second part, a number of almost-everywhere convergence theorems are looked at using computable analysis and algorithmic randomness. These include various martingale convergence theorems and almosteverywhere differentiability theorems. General condit

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Birch, Thomas. "Algorithmic randomness on computable metric spaces and hyperspaces." Master's thesis, University of Cape Town, 2012. http://hdl.handle.net/11427/22093.

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In this text we shall be focusing on generalizing Martin-Löf randomness to computable metric spaces with arbitrary measure (for examples of this type of generalization see Gács [14], Rojas and Hoyrup [15]. The aim of this generalization is to define algorithmic randomness on the hyperspace of non-empty compact subsets of a computable metric space, the study of which was first proposed by Barmpalias et al. [16] at the University of Florida in their work on the random closed subsets of the Cantor space. Much work has been done in the study of random sets with authors such as Diamondstone and Kjo

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Kenny, Robert. "Orbit complexity and computable Markov partitions." University of Western Australia. School of Mathematics and Statistics, 2008. http://theses.library.uwa.edu.au/adt-WU2008.0231.

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Markov partitions provide a 'good' mechanism of symbolic dynamics for uniformly hyperbolic systems, forming the classical foundation for the thermodynamic formalism in this setting, and remaining useful in the modern theory. Usually, however, one takes Bowen's 1970's general construction for granted, or restricts to cases with simpler geometry (as on surfaces) or more algebraic structure. This thesis examines several questions on the algorithmic content of (topological) Markov partitions, starting with the pointwise, entropy-like, topological conjugacy invariant known as orbit complexity. The

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Beaulieu, Jason. "A Dynamic, Interactive Approach to Learning Engineering and Mathematics." Thesis, Virginia Tech, 2012. http://hdl.handle.net/10919/32165.

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The major objectives of this thesis involve the development of both dynamic and interactive applications aimed at complementing traditional engineering and science coursework, laboratory exercises, research, and providing users with easy access by publishing the applications on Wolframs Demonstration website. A number of applications have been carefully designed to meet cognitive demands as well as provide easy-to-use interactivity. Recent technology introduced by Wolfram Mathematica called CDF (Computable Document Format) provides a resource that gives ideas a communication pipeline in which

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Dahlgren, Fredrik. "Effective Distribution Theory." Doctoral thesis, Uppsala : Department of Mathematics, Uppsala University, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8210.

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Dillhage, Ruth [Verfasser]. "Computable functional analysis : compact operators on computable banach spaces and computable best approximation / Ruth Dillhage." Hagen : Fernuniversität Hagen, 2012. http://d-nb.info/1025601831/34.

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Karadais, Basil A. "Towards an arithmetic for partial computable functionals." Diss., Ludwig-Maximilians-Universität München, 2013. http://nbn-resolving.de/urn:nbn:de:bvb:19-163281.

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The thesis concerns itself with nonflat Scott information systems as an appropriate denotational semantics for the proposed theory TCF+, a constructive theory of higher-type partial computable functionals and approximations. We prove a definability theorem for type systems with at most unary constructors via atomic-coherent information systems, and give a simple proof for the density property for arbitrary finitary type systems using coherent information systems. We introduce the notions of token matrices and eigen-neighborhoods, and use them to locate normal forms of neighborhoods, as well as

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Karádais, Basil A. [Verfasser], and Helmut [Akademischer Betreuer] Schwichtenberg. "Towards an arithmetic for partial computable functionals / Basil A. Karadais. Betreuer: Helmut Schwichtenberg." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2013. http://d-nb.info/1047543400/34.

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Karádais, Basil A. Verfasser], and Helmut [Akademischer Betreuer] [Schwichtenberg. "Towards an arithmetic for partial computable functionals / Basil A. Karadais. Betreuer: Helmut Schwichtenberg." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2013. http://nbn-resolving.de/urn:nbn:de:bvb:19-163281.

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Palaparambil, Dinesh Lakshmi. "Essays on Mathematical Optimization for Residential Demand Response in the Energy Sector." University of Cincinnati / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1511860511116905.

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Books on the topic "Computable mathematics"

1

Epstein, Richard L. Computability: Computable functions, logic, and the foundations of mathematics. Brooks/Cole Advanced Books & Software, 1988.

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Epstein, Richard L. Computability: Computable functions, logic, and the foundations of mathematics. 2nd ed. Wadsworth/Thomson Learning, 2000.

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Epstein, Richard L. Computability: Computable functions, logic, and the foundations of mathematics. Wadsworth & Brooks/Cole Advanced Books & Software, 1989.

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Computable economics: The Arne Ryde memorial lectures. Oxford University Press, 2000.

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Epstein, Richard L. Computability: Computable functions, logic, and the foundations of mathematics. 3rd ed. Advanced Reasoning Forum, 2008.

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6

Berardi, Stefano. A sequent calculus for limit computable mathematics (technical report). Sangyō Gijutsu Sōgō Kenkyūjo Shisutemu Kenshō Kenkyū Sentā., 2006.

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7

Tourlakis, George J. Theory of computation. Wiley, 2012.

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France, Société mathématique de, ed. Interactive models of computation and program behavior. Société mathématique de France, 2009.

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9

Cooper, S. B., and Andrea Sorbi. Computability in context: Computation and logic in the real world. World Scientific, 2011.

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10

Hilbert's tenth problem. MIT Press, 1993.

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Book chapters on the topic "Computable mathematics"

1

Hayashi, Susumu, and Masahiro Nakata. "Towards Limit Computable Mathematics." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45842-5_9.

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Solomon, Reed. "Computable Reductions and Reverse Mathematics." In Pursuit of the Universal. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-40189-8_19.

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Hirschfeldt, Denis R. "Some Questions in Computable Mathematics." In Computability and Complexity. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-50062-1_4.

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Hayashi, Susumu, and Yohji Akama. "Limit-Computable Mathematics and Its Applications." In Computer Science Logic. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45793-3_1.

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Boylan, Thomas A., and Paschal F. O’Gorman. "The emergence of constructive and computable mathematics." In Philosophy of Mathematics and Economics. Routledge, 2018. http://dx.doi.org/10.4324/9781351124584-8.

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Ceberio, Martine, Olga Kosheleva, and Vladik Kreinovich. "Reverse Mathematics Is Computable for Interval Computations." In Studies in Systems, Decision and Control. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-40814-5_8.

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Repin, S., and T. Samrowski. "On Computable Bounds of Modeling Errors." In Numerical Mathematics and Advanced Applications 2011. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-33134-3_6.

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Weisstein, Eric. "Computable Data, Mathematics, and Digital Libraries in Mathematica and Wolfram|Alpha." In Lecture Notes in Computer Science. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08434-3_3.

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Zheng, Xizhong, and George Barmpalias. "On the Monotonic Computability of Semi-computable Real Numbers." In Discrete Mathematics and Theoretical Computer Science. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-45066-1_23.

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Bucciarelli, Edgardo, and Nicola Mattoscio. "Recasting Stefano Zambelli: Notes on the Foundations of Mathematics for a Post-Neoclassical Age in Economics." In Keynesian, Sraffian, Computable and Dynamic Economics. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-58131-2_3.

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Conference papers on the topic "Computable mathematics"

1

Issakhov, Assylbek. "Hyperimmunity and A-computable universal numberings." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4959720.

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Russell, Daniel A. "Creating interactive acoustics animations using Mathematica's Computable Document Format." In ICA 2013 Montreal. ASA, 2013. http://dx.doi.org/10.1121/1.4801411.

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